Related papers: Global parameter test ideals

We describe an algorithm for computing parameter-test-ideals in certain local Cohen-Macaulay rings. The algorithm is based on the study of a Frobenius map on the injective hull of the residue field of the ring and on the application of…

The third named author and P\'{e}rez proved that under certain conditions the test ideal of a module closure agrees with the trace ideal of the module closure. We use this fact to compute the test ideals of various rings with respect to the…

Motivated by recent result of P\'erez and R.G. on equality of test ideal of module closure operation and trace ideal, and the well-known result by Smith that parameter test ideal cannot be contained in parameter ideals, we study the…

We construct a local Cohen-Macaulay ring $R$ with a prime ideal $\mathfrak{p}\in\spec(R)$ such that $R$ satisfies the uniform Auslander condition (UAC), but the localization $R_{\mathfrak{p}}$ does not satisfy Auslander's condition (AC).…

We find sufficient conditions which imply equality of the finitistic test ideal and test ideal in rings of prime characteristic. Utilizing recent progress from the prime characteristic minimal model program we equate the notions of…

In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be treated as part of the theory of GGL rings. For a…

Let $k$ be a field. We determine the ideals $I$ in a finitely generated graded $k$-algebra $A$, whose associated graded rings are isomorphic to $A$. Also we compute the graded local cohomologies of the Rees rings $A[I t]$ and give the…

In this paper, we consider whether parameter test ideals, conductors, $F$-ideals, and trace ideals are contained in an ideal whose quotient ring has finite phantom projective dimension (for example, ideals generated by a system of…

Let $M$ be a finite module over a commutative noetherian ring $R$. For ideals $\fa$ and $\fb$ of $R$, the relations between cohomological dimensions of $M$ with respect to $\fa, \fb$, $\fa\cap\fb$ and $\fa+ \fb$ are studied. When $R$ is…

Let $(R, {\frak m})$ be a local ring, $I$ a proper ideal of $R$ and $M$ a finitely generated $R$-module of dimension $d$. We discuss the local homology modules of $H^d_I(M)$. When $M$ is Cohen-Macaulay, it is proved that $H^d_{{\frak…

In this paper we consider the problem of finding explicitly canonical ideals of one-dimensional Cohen-Macaulay local rings. We show that Gorenstein ideals contained in a high power of the maximal ideal are canonical ideals. In the…

This paper studies Frobenius powers of parameter ideals in a commutative Noetherian local ring $R$ of prime characteristic $p$. For a given ideal $\fa$ of $R$, there is a power $Q$ of $p$, depending on $\fa$, such that the $Q$-th Frobenius…

We recall a numerical criteria for Cohen--Macaulayness related to system of parameters, and introduce monomial ideals of K\"onig type which include the edge ideals of K\"onig graphs. We show that a monomial ideal is of K\"onig type if and…

In this paper, the structure of the ideals in the ring of Colombeau generalized numbers is investigated. Connections with the theories of exchange rings, Gelfand rings and lattice-ordered rings are given. Characterizations for prime,…

In this paper we present a technical lemma about localization at countable infinitely many prime ideals. We apply this lemma to get many results about the finiteness of associated prime ideals of local cohomology modules.

Let $(R, \mathfrak m)$ be an unmixed Noetherian local ring, Q a parameter ideal and $K$ an $\mathfrak m$-primary ideal of $R$ containing $Q$. We give a necessary and sufficient condition for $R$ to be Cohen-Macaulay in terms of $g_0(Q)$ and…

In this paper we prove the existence of a uniform bound for Frobenius test exponents for parameter ideals of a local ring $(R, \frak m)$ of prime characteristic in the following cases: (1) $R$ is generalized Cohen-Macaulay. Our proof is…

Let $R$ be a noetherian local ring. We consider the following quastion: Does there exist an integer $n$ such that all idelas generated by a system of parameters contained in the $n$-th power of the maximal ideal have the same Betti numbers?…

In the present paper we investigate a question stemming from a long-standing conjecture of Vasconcelos: given a generically a complete intersection perfect ideal I in a regular local ring R, is it true that if I/I^2 (or R/I^2) is…

We provide a natural criterion which implies equality of the finitistic test ideal and test ideal in local rings of prime characteristic. Most notably, we show that the criterion is met by every local weakly $F$-regular ring whose…